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Diffusion-Weighted and NMR Imaging of Porous Media

A non-invasive study of translational dynamics requires a kind of "marking" or "labeling" of the traveling atoms or molecules for tracing their displacements. Magnetic field is a superb experimental tool for encoding the motion of spin-bearing particles. Moreover, since a geometrical confinement considerably affects diffusive motion, the geometry of porous media can be indirectly accessed by measuring the signal attenuation due to restricted diffusion in inhomogeneous magnetic fields. In this talk, we focus on some theoretical and numerical aspects of this problem. Starting from the classical Bloch-Torrey equation, we obtain the NMR signal in a compact matrix form. Each attenuation mechanism (restricted diffusion, gradient dephasing, surface or bulk relaxation) is represented by a matrix which is constructed from the Laplace operator eigenbasis and thus depending only on the geometry of the confinement. In turn, the physical parameters (free diffusion coefficient, gradient intensity, surface or bulk relaxivity) characterize the "strengths" of the underlying attenuation mechanisms and naturally appear as coefficients in front of these matrices. We illustrate the use of this matrix technique by considering restricted diffusion in simple domains: a slab, a cylinder, and a sphere. Further investigation of irregularly-shaped confinements is discussed.

Location: Hedco Pertroleum and Chemical Engineering Building (HED) - 116

Audiences: Everyone Is Invited

Contact: Petra Pearce Sapir